Safe Haskell	Safe-Inferred
Language	Haskell2010

Posit

Contents

Main Exported Types
A Complete Pair of Patterns for Matching Exported Types
Fused Operation Interface defined by the Posit Standard
Posits are Convertable between different Posit representations
Additional functions to show the Posit in different formats
Additional Special Functions
Functions to lift functions of Integers or Rationals to operate on Posit Types

Description

Library implementing standard Posit Numbers both Posit Standard version 3.2 and 2022, with some improvements. Posit is the interface, PositC provides the implemetation. 2's Complement Fixed Point Integers, and Rational numbers, are used throughout, as well as Integers & Naturals. Encode and Decode are indexed through a Type Family.

Synopsis

data Posit (es :: ES)
type Posit8 = Posit Z_3_2
type Posit16 = Posit I_3_2
type Posit32 = Posit II_3_2
type Posit64 = Posit III_3_2
type Posit128 = Posit IV_3_2
type Posit256 = Posit V_3_2
type P8 = Posit Z_2022
type P16 = Posit I_2022
type P32 = Posit II_2022
type P64 = Posit III_2022
type P128 = Posit IV_2022
type P256 = Posit V_2022
pattern NaR :: forall es. PositC es => Posit es
pattern R :: forall es. PositC es => Rational -> Posit es
class Num a => FusedOps a where
- fma :: a -> a -> a -> a
- fam :: a -> a -> a -> a
- fmms :: a -> a -> a -> a -> a
- fsum3 :: a -> a -> a -> a
- fsum4 :: a -> a -> a -> a -> a
- fsumL :: Foldable t => t a -> a
- fdot3 :: a -> a -> a -> a -> a -> a -> a
- fdot4 :: a -> a -> a -> a -> a -> a -> a -> a -> a
- fdotL :: Foldable t => t a -> t a -> a
- fsm :: a -> a -> a -> a
class Convertible a b where
- convert :: a -> b
class AltShow a where
- displayBinary :: a -> String
- displayIntegral :: a -> String
- displayRational :: a -> String
- displayDecimal :: a -> String
class AltFloating p where
- machEps :: p
- approxEq :: p -> p -> Bool
- goldenRatio :: p
- hypot2 :: p -> p -> p
- hypot3 :: p -> p -> p -> p
- hypot4 :: p -> p -> p -> p -> p
viaIntegral :: PositC es => (IntN es -> IntN es) -> Posit es -> Posit es
viaRational :: PositC es => (Rational -> Rational) -> Posit es -> Posit es
viaRational2 :: PositC es => (Rational -> Rational -> Rational) -> Posit es -> Posit es -> Posit es
viaRational3 :: PositC es => (Rational -> Rational -> Rational -> Rational) -> Posit es -> Posit es -> Posit es -> Posit es
viaRational4 :: PositC es => (Rational -> Rational -> Rational -> Rational -> Rational) -> Posit es -> Posit es -> Posit es -> Posit es -> Posit es
viaRational6 :: PositC es => (Rational -> Rational -> Rational -> Rational -> Rational -> Rational -> Rational) -> Posit es -> Posit es -> Posit es -> Posit es -> Posit es -> Posit es -> Posit es
viaRational8 :: PositC es => (Rational -> Rational -> Rational -> Rational -> Rational -> Rational -> Rational -> Rational -> Rational) -> Posit es -> Posit es -> Posit es -> Posit es -> Posit es -> Posit es -> Posit es -> Posit es -> Posit es

Documentation

data Posit (es :: ES) Source #

Base GADT rapper type, that uses the Exponent Size kind to index the various implementations

Instances

Instances details

PositC es => Storable (Posit es) Source #
Instance details Defined in Posit Methods sizeOf :: Posit es -> Int # alignment :: Posit es -> Int # peekElemOff :: Ptr (Posit es) -> Int -> IO (Posit es) # pokeElemOff :: Ptr (Posit es) -> Int -> Posit es -> IO () # peekByteOff :: Ptr b -> Int -> IO (Posit es) # pokeByteOff :: Ptr b -> Int -> Posit es -> IO () # peek :: Ptr (Posit es) -> IO (Posit es) # poke :: Ptr (Posit es) -> Posit es -> IO () #
PositC es => Bounded (Posit es) Source #
Instance details Defined in Posit Methods minBound :: Posit es # maxBound :: Posit es #
PositC es => Enum (Posit es) Source #
Instance details Defined in Posit Methods succ :: Posit es -> Posit es # pred :: Posit es -> Posit es # toEnum :: Int -> Posit es # fromEnum :: Posit es -> Int # enumFrom :: Posit es -> [Posit es] # enumFromThen :: Posit es -> Posit es -> [Posit es] # enumFromTo :: Posit es -> Posit es -> [Posit es] # enumFromThenTo :: Posit es -> Posit es -> Posit es -> [Posit es] #
PositF es => Floating (Posit es) Source #
Instance details Defined in Posit Methods pi :: Posit es # exp :: Posit es -> Posit es # log :: Posit es -> Posit es # sqrt :: Posit es -> Posit es # (**) :: Posit es -> Posit es -> Posit es # logBase :: Posit es -> Posit es -> Posit es # sin :: Posit es -> Posit es # cos :: Posit es -> Posit es # tan :: Posit es -> Posit es # asin :: Posit es -> Posit es # acos :: Posit es -> Posit es # atan :: Posit es -> Posit es # sinh :: Posit es -> Posit es # cosh :: Posit es -> Posit es # tanh :: Posit es -> Posit es # asinh :: Posit es -> Posit es # acosh :: Posit es -> Posit es # atanh :: Posit es -> Posit es # log1p :: Posit es -> Posit es # expm1 :: Posit es -> Posit es # log1pexp :: Posit es -> Posit es # log1mexp :: Posit es -> Posit es #
(Floating (Posit es), PositC es) => RealFloat (Posit es) Source #
Instance details Defined in Posit Methods floatRadix :: Posit es -> Integer # floatDigits :: Posit es -> Int # floatRange :: Posit es -> (Int, Int) # decodeFloat :: Posit es -> (Integer, Int) # encodeFloat :: Integer -> Int -> Posit es # exponent :: Posit es -> Int # significand :: Posit es -> Posit es # scaleFloat :: Int -> Posit es -> Posit es # isNaN :: Posit es -> Bool # isInfinite :: Posit es -> Bool # isDenormalized :: Posit es -> Bool # isNegativeZero :: Posit es -> Bool # isIEEE :: Posit es -> Bool # atan2 :: Posit es -> Posit es -> Posit es #
PositC es => Num (Posit es) Source #
Instance details Defined in Posit Methods (+) :: Posit es -> Posit es -> Posit es # (-) :: Posit es -> Posit es -> Posit es # (*) :: Posit es -> Posit es -> Posit es # negate :: Posit es -> Posit es # abs :: Posit es -> Posit es # signum :: Posit es -> Posit es # fromInteger :: Integer -> Posit es #
PositC es => Read (Posit es) Source #
Instance details Defined in Posit Methods readsPrec :: Int -> ReadS (Posit es) # readList :: ReadS [Posit es] # readPrec :: ReadPrec (Posit es) # readListPrec :: ReadPrec [Posit es] #
PositC es => Fractional (Posit es) Source #
Instance details Defined in Posit Methods (/) :: Posit es -> Posit es -> Posit es # recip :: Posit es -> Posit es # fromRational :: Rational -> Posit es #
PositC es => Real (Posit es) Source #
Instance details Defined in Posit Methods toRational :: Posit es -> Rational #
PositC es => RealFrac (Posit es) Source #
Instance details Defined in Posit Methods properFraction :: Integral b => Posit es -> (b, Posit es) # truncate :: Integral b => Posit es -> b # round :: Integral b => Posit es -> b # ceiling :: Integral b => Posit es -> b # floor :: Integral b => Posit es -> b #
PositC es => Show (Posit es) Source #
Instance details Defined in Posit Methods showsPrec :: Int -> Posit es -> ShowS # show :: Posit es -> String # showList :: [Posit es] -> ShowS #
NFData (Posit es) Source #	NFData Instance
Instance details Defined in Posit Methods rnf :: Posit es -> () #
PositC es => Eq (Posit es) Source #
Instance details Defined in Posit Methods (==) :: Posit es -> Posit es -> Bool # (/=) :: Posit es -> Posit es -> Bool #
PositC es => Ord (Posit es) Source #
Instance details Defined in Posit Methods compare :: Posit es -> Posit es -> Ordering # (<) :: Posit es -> Posit es -> Bool # (<=) :: Posit es -> Posit es -> Bool # (>) :: Posit es -> Posit es -> Bool # (>=) :: Posit es -> Posit es -> Bool # max :: Posit es -> Posit es -> Posit es # min :: Posit es -> Posit es -> Posit es #
PositF es => AltFloating (Posit es) Source #
Instance details Defined in Posit Methods machEps :: Posit es Source # approxEq :: Posit es -> Posit es -> Bool Source # goldenRatio :: Posit es Source # hypot2 :: Posit es -> Posit es -> Posit es Source # hypot3 :: Posit es -> Posit es -> Posit es -> Posit es Source # hypot4 :: Posit es -> Posit es -> Posit es -> Posit es -> Posit es Source #
PositC es => AltShow (Posit es) Source #
Instance details Defined in Posit Methods displayBinary :: Posit es -> String Source # displayIntegral :: Posit es -> String Source # displayRational :: Posit es -> String Source # displayDecimal :: Posit es -> String Source #
PositC es => FusedOps (Posit es) Source #
Instance details Defined in Posit Methods fma :: Posit es -> Posit es -> Posit es -> Posit es Source # fam :: Posit es -> Posit es -> Posit es -> Posit es Source # fmms :: Posit es -> Posit es -> Posit es -> Posit es -> Posit es Source # fsum3 :: Posit es -> Posit es -> Posit es -> Posit es Source # fsum4 :: Posit es -> Posit es -> Posit es -> Posit es -> Posit es Source # fsumL :: Foldable t => t (Posit es) -> Posit es Source # fdot3 :: Posit es -> Posit es -> Posit es -> Posit es -> Posit es -> Posit es -> Posit es Source # fdot4 :: Posit es -> Posit es -> Posit es -> Posit es -> Posit es -> Posit es -> Posit es -> Posit es -> Posit es Source # fdotL :: Foldable t => t (Posit es) -> t (Posit es) -> Posit es Source # fsm :: Posit es -> Posit es -> Posit es -> Posit es Source #
PositC es => Random (Posit es) Source #	Random instance for the Posit Sampling of R [0,1), this is for the real numbers, not on the projective real numbers, for projective real numbers, use Uniform.
Instance details Defined in Posit Methods randomR :: RandomGen g => (Posit es, Posit es) -> g -> (Posit es, g) # random :: RandomGen g => g -> (Posit es, g) # randomRs :: RandomGen g => (Posit es, Posit es) -> g -> [Posit es] # randoms :: RandomGen g => g -> [Posit es] #
PositC es => Uniform (Posit es) Source #	Uniform instance for the Posit Sampling of the projective real line
Instance details Defined in Posit Methods uniformM :: StatefulGen g m => g -> m (Posit es) #
(PositC es1, PositC es2) => Convertible (Posit es1) (Posit es2) Source #
Instance details Defined in Posit Methods convert :: Posit es1 -> Posit es2 Source #

Main Exported Types

type Posit8 = Posit Z_3_2 Source #

A Posit-3.2 8-bit Posit number with exponentSize = '0', and 1 byte wide

type Posit16 = Posit I_3_2 Source #

A Posit-3.2 16-bit Posit number with exponentSize = '1', and 2 bytes wide

type Posit32 = Posit II_3_2 Source #

A Posit-3.2 32-bit Posit number with exponentSize = '2', and 4 bytes wide

type Posit64 = Posit III_3_2 Source #

A Posit-3.2 64-bit Posit number with exponentSize = '3', and 8 bytes wide

type Posit128 = Posit IV_3_2 Source #

A Posit-3.2 128-bit Posit number with exponentSize = '4', and 16 bytes wide

type Posit256 = Posit V_3_2 Source #

A Posit-3.2 256-bit Posit number with exponentSize = '5', and 32 bytes wide

type P8 = Posit Z_2022 Source #

A Posit-2022 8-bit Posit number with exponentSize = '2', and 1 byte wide

type P16 = Posit I_2022 Source #

A Posit-2022 16-bit Posit number with exponentSize = '2', and 2 bytes wide

type P32 = Posit II_2022 Source #

A Posit-2022 32-bit Posit number with exponentSize = '2', and 4 bytes wide

type P64 = Posit III_2022 Source #

A Posit-2022 64-bit Posit number with exponentSize = '2', and 8 bytes wide

type P128 = Posit IV_2022 Source #

A Posit-2022 128-bit Posit number with exponentSize = '2', and 16 bytes wide

type P256 = Posit V_2022 Source #

A Posit-2022 256-bit Posit number with exponentSize = '2', and 32 bytes wide

A Complete Pair of Patterns for Matching Exported Types

pattern NaR :: forall es. PositC es => Posit es Source #

Not a Real Number, the Posit is like a Maybe type, it's either a real number or not

A pattern for Exception handling when a value is Not a Real number (NaR).

pattern R :: forall es. PositC es => Rational -> Posit es Source #

A Real or at least Rational Number, rounded to the nearest Posit Rational representation

A pattern for the non-Exceptional case, yielding a Rational, will make a total function when paired with NaR, if the Rational implementation is total.

Fused Operation Interface defined by the Posit Standard

class Num a => FusedOps a where Source #

A class that delays the rounding operation until the end for some operations

Methods

fma :: a -> a -> a -> a Source #

Fused Multiply Add: (a * b) + c

fam :: a -> a -> a -> a Source #

Fused Add Multiply: (a + b) * c

fmms :: a -> a -> a -> a -> a Source #

Fused Multiply Multiply Subtract: (a * b) - (c * d)

fsum3 :: a -> a -> a -> a Source #

Fused Sum of 3 values: a + b + c

fsum4 :: a -> a -> a -> a -> a Source #

Fused Sum of 4 values: a + b + c + d

fsumL :: Foldable t => t a -> a Source #

Fused Sum of a List of Posits

fdot3 :: a -> a -> a -> a -> a -> a -> a Source #

Fused Dot Product of 3 element vector: (a1 * b1) + (a2 * b2) + (a3 * b3)

fdot4 :: a -> a -> a -> a -> a -> a -> a -> a -> a Source #

Fused Dot Product of 4 element vector: (a0 * b0) + (a1 * b1) + (a2 * b2) + (a3 * b3)

fdotL :: Foldable t => t a -> t a -> a Source #

Fused Dot Product of Two Lists

fsm :: a -> a -> a -> a Source #

Fused Subtract Multiply: a - (b * c)

Instances

Instances details

FusedOps Rational Source #
Instance details Defined in Posit Methods fma :: Rational -> Rational -> Rational -> Rational Source # fam :: Rational -> Rational -> Rational -> Rational Source # fmms :: Rational -> Rational -> Rational -> Rational -> Rational Source # fsum3 :: Rational -> Rational -> Rational -> Rational Source # fsum4 :: Rational -> Rational -> Rational -> Rational -> Rational Source # fsumL :: Foldable t => t Rational -> Rational Source # fdot3 :: Rational -> Rational -> Rational -> Rational -> Rational -> Rational -> Rational Source # fdot4 :: Rational -> Rational -> Rational -> Rational -> Rational -> Rational -> Rational -> Rational -> Rational Source # fdotL :: Foldable t => t Rational -> t Rational -> Rational Source # fsm :: Rational -> Rational -> Rational -> Rational Source #
PositC es => FusedOps (Posit es) Source #
Instance details Defined in Posit Methods fma :: Posit es -> Posit es -> Posit es -> Posit es Source # fam :: Posit es -> Posit es -> Posit es -> Posit es Source # fmms :: Posit es -> Posit es -> Posit es -> Posit es -> Posit es Source # fsum3 :: Posit es -> Posit es -> Posit es -> Posit es Source # fsum4 :: Posit es -> Posit es -> Posit es -> Posit es -> Posit es Source # fsumL :: Foldable t => t (Posit es) -> Posit es Source # fdot3 :: Posit es -> Posit es -> Posit es -> Posit es -> Posit es -> Posit es -> Posit es Source # fdot4 :: Posit es -> Posit es -> Posit es -> Posit es -> Posit es -> Posit es -> Posit es -> Posit es -> Posit es Source # fdotL :: Foldable t => t (Posit es) -> t (Posit es) -> Posit es Source # fsm :: Posit es -> Posit es -> Posit es -> Posit es Source #

Posits are Convertable between different Posit representations

class Convertible a b where Source #

A Convertible class that will cast or convert between two different Posit es types

Methods

convert :: a -> b Source #

Instances

Instances details

(PositC es1, PositC es2) => Convertible (Posit es1) (Posit es2) Source #
Instance details Defined in Posit Methods convert :: Posit es1 -> Posit es2 Source #

Additional functions to show the Posit in different formats

class AltShow a where Source #

A Alternative to the typical Show class to assist in displaying the Posit es type in different formats

Methods

displayBinary :: a -> String Source #

Display the Posit in its Binary Representation

displayIntegral :: a -> String Source #

Display the Posit in its Integral Representation

displayRational :: a -> String Source #

Display the Posit as a Rational

displayDecimal :: a -> String Source #

Display the Posit as a Decimal until the Repetend occurs

Instances

Instances details

PositC es => AltShow (Posit es) Source #
Instance details Defined in Posit Methods displayBinary :: Posit es -> String Source # displayIntegral :: Posit es -> String Source # displayRational :: Posit es -> String Source # displayDecimal :: Posit es -> String Source #

Additional Special Functions

class AltFloating p where Source #

Methods

machEps :: p Source #

approxEq :: p -> p -> Bool Source #

goldenRatio :: p Source #

hypot2 :: p -> p -> p Source #

hypot3 :: p -> p -> p -> p Source #

hypot4 :: p -> p -> p -> p -> p Source #

Instances

Instances details

PositF es => AltFloating (Posit es) Source #
Instance details Defined in Posit Methods machEps :: Posit es Source # approxEq :: Posit es -> Posit es -> Bool Source # goldenRatio :: Posit es Source # hypot2 :: Posit es -> Posit es -> Posit es Source # hypot3 :: Posit es -> Posit es -> Posit es -> Posit es Source # hypot4 :: Posit es -> Posit es -> Posit es -> Posit es -> Posit es Source #

Functions to lift functions of Integers or Rationals to operate on Posit Types

viaIntegral :: PositC es => (IntN es -> IntN es) -> Posit es -> Posit es Source #

viaRational :: PositC es => (Rational -> Rational) -> Posit es -> Posit es Source #

viaRational2 :: PositC es => (Rational -> Rational -> Rational) -> Posit es -> Posit es -> Posit es Source #

viaRational3 :: PositC es => (Rational -> Rational -> Rational -> Rational) -> Posit es -> Posit es -> Posit es -> Posit es Source #

viaRational4 :: PositC es => (Rational -> Rational -> Rational -> Rational -> Rational) -> Posit es -> Posit es -> Posit es -> Posit es -> Posit es Source #

viaRational6 :: PositC es => (Rational -> Rational -> Rational -> Rational -> Rational -> Rational -> Rational) -> Posit es -> Posit es -> Posit es -> Posit es -> Posit es -> Posit es -> Posit es Source #

viaRational8 :: PositC es => (Rational -> Rational -> Rational -> Rational -> Rational -> Rational -> Rational -> Rational -> Rational) -> Posit es -> Posit es -> Posit es -> Posit es -> Posit es -> Posit es -> Posit es -> Posit es -> Posit es Source #